Modified Born Approximation and the Elastic Scattering of Electrons from Helium

Abstract

We discuss the elastic scattering of electrons from helium atoms in terms of an energy-dependent central-potential model having the form $V\left(r\right)=2Zlimit\; of\left(\frac{-{\Lambda }^2}{{\Lambda }^2-{\mu }^2}\frac{e^{-\mu r}}{r}+\frac{{\mu }^2}{{\Lambda }^2-{\mu }^2}\frac{e^{-\Lambda r}}{r}\right)-\frac{\alpha }{{(r^2+d^2)}^2}\text{as}\Lambda \to \mu ,$ where $\mu ,\alpha$ are fixed constants (for He, $\mu =3.375\mathrm{}$ and $\alpha =1.39\mathrm{}$), and $d$ is an energy-dependent phenomenological parameter. The method of partial waves is adapted for a generalized Yukawa potential and a polarization potential. Phase shifts and scattering cross sections are calculated from our potential model using the first Born approximation and a modified form of it. We develop an effective-range theory for a generalized Yukawa and a polarization potential, and apply it to generate a set of energy-dependent electron-helium phase shifts in the region 0-500 eV. Recent experimental angular distribution data in the region 100-500 eV are rather satisfactorily accounted for by our potential model. Our results compare favorably with those of LaBahn and Callaway.